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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 30, Iss. 7 — Jul. 1, 2013
  • pp: 1387–1393

Nonlocal optical effects on the Goos–Hänchen shift at an interface of a composite material of metallic nanoparticles

J. H. Huang and P. T. Leung  »View Author Affiliations

JOSA A, Vol. 30, Issue 7, pp. 1387-1393 (2013)

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We present a theoretical study on the nonlocal optical effects on the Goos–Hänchen (GH) shift of reflected light from a composite material of metallic nanoparticles (MNPs). Using different nonlocal effective medium models, it is observed that such effects can be significant for small MNP of sizes down to a few nanometers. For small metallic volume fractions, the composite behaves like dielectric and the nonlocal effects lead to significant different Brewster angles, at which large negative GH shifts take place. For larger volume fractions or shorter wavelengths, the composite behaves more like metals and the nonlocal effects also lead to different Brewster angles but at values close to grazing incidence. These results will have significant implications in the application of different effective medium models for the characterization of these nanometallic composites when the MNPs are down to a few nanometers in size.

© 2013 Optical Society of America

OCIS Codes
(120.5700) Instrumentation, measurement, and metrology : Reflection
(240.0240) Optics at surfaces : Optics at surfaces
(260.2110) Physical optics : Electromagnetic optics
(260.2065) Physical optics : Effective medium theory
(260.2710) Physical optics : Inhomogeneous optical media

ToC Category:
Physical Optics

Original Manuscript: May 2, 2013
Manuscript Accepted: May 14, 2013
Published: June 24, 2013

J. H. Huang and P. T. Leung, "Nonlocal optical effects on the Goos–Hänchen shift at an interface of a composite material of metallic nanoparticles," J. Opt. Soc. Am. A 30, 1387-1393 (2013)

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  1. F. Goos and H. Hänchen, “Ein neuer und fundamentalerVersuch zur Totalreflexion,” Ann. Phys. 436, 333–346 (1947). [CrossRef]
  2. W. J. Wild and C. L. Giles, “Goos–Hänchen shifts from absorbing media,” Phys. Rev. A 25, 2099–2101 (1982). [CrossRef]
  3. For the latest reviews, see the recent special issue on “Beam shifts,” J. Opt.15(1), 014001 (2013).
  4. B. Zhao and L. Gao, “Temperature-dependent Goos–Hänchen shift on the interface of metal/dielectric composites,” Opt. Express 17, 21433–21441 (2009). [CrossRef]
  5. D. Gao and L. Gao, “Goos–Hänchen shift of the reflection from nonlinear nanocomposites with electric field tenability,” Appl. Phys. Lett. 97, 041903 (2010). [CrossRef]
  6. C. W. Chen, Y. W. Gu, H. P. Chiang, E. J. Sanchez, and P. T. Leung, “Goos–Hänchen shift at an interface of a composite material: effects of particulate clustering,” Appl. Phys. B 104, 647–652 (2011). [CrossRef]
  7. Y. Huang, B. Zhao, and L. Gao, “Goos–Hänchen shift of the reflected wave through an anisotropic metamaterial containing metal/dielectric nanocomposites,” J. Opt. Soc. Am. A 29, 1436–1444 (2012). [CrossRef]
  8. R. Ruppin, “Optical properties of small metal spheres,” Phys. Rev. B 11, 2871–2876 (1975). [CrossRef]
  9. B. B. Dasgupta and R. Fuchs, “Polarizability of a small sphere including nonlocal effect,” Phys. Rev. B 24, 554–561 (1981). [CrossRef]
  10. R. Fuchs and F. Claro, “Multipolar response of small metallic spheres: nonlocal theory,” Phys. Rev. B 35, 3722–3727 (1987). [CrossRef]
  11. S. P. Apell, A. Ljungbert, and S. Lundqvist, “Nonlocal optical effects at metal surfaces,” Phys. Scr. 30, 367–383 (1984). [CrossRef]
  12. S. P. Apell, J. Giraldo, and S. Lundqvist, “Small metal particles: nonlocal optical properties and quantum-sizeeffects,” Phase Transit. 2626, 511–604 (1990).
  13. G. S. Agarwal and R. Inguva, “Effective-medium theory of a heterogeneous medium with individual grains having a nonlocal dielectric function,” Phys. Rev. B 30, 6108–6117 (1984). [CrossRef]
  14. R. Chang, H. P. Chiang, P. T. Leung, D. P. Tsai, and W. S. Tse, “Nonlocal effects in the optical response of composite materials with metallic nanoparticles,” Solid State Commun. 133, 315–320 (2005). [CrossRef]
  15. J. C. Maxwell-Garnett, “Colours in metal glasses and in metallic films,” Philos. Trans. R. Soc. London 203, 385–420 (1904). [CrossRef]
  16. J. C. Maxwell-Garnett, “Colours in metal glasses and in metallic films, and in metallic solutions,” Philos. Trans. R. Soc. London 205, 237–288 (1906). [CrossRef]
  17. D. A. G. Bruggeman, “Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen,” Ann. Phys. 24, 636–664 (1935). [CrossRef]
  18. C. W. Chen, H. Y. Chung, H. P. Chiang, J. Y. Lu, R. Chang, D. P. Tsai, and P. T. Leung, “Nonlocality and particle-clustering effects on the optical response of composite materials with metallic nanoparticles,” Appl. Phys. A 101, 191–198 (2010). [CrossRef]
  19. J. L. Birman, D. N. Pattanayak, and A. Puri, “Prediction of a resonance-enhanced laser-beam displacement at total internal reflection in semiconductors,” Phys. Rev. Lett. 50, 1664–1667 (1983). [CrossRef]
  20. A. Puri and D. N. Pattanayak, “Resonance effects on total internal reflection and lateral (Goos–Hänchen) beam displacement at the interface between nonlocal and local dielectric,” Phys. Rev. B 28, 5877–5886 (1983). [CrossRef]
  21. A. Puri and J. L. Birman, “Goos–Hänchen beam shift at total internal reflection with application to spatially dispersive media,” J. Opt. Soc. Am. A 3, 543–549 (1986). [CrossRef]
  22. R. Chang, H. P. Chiang, P. T. Leung, and W. S. Tse, “Nonlocal electrodynamic effects in the optical excitation of the surface plasmon resonance,” Opt. Commun. 225, 353–361 (2003). [CrossRef]
  23. T. C. Choy, Effective Medium Theory (Clarendon, 1999).
  24. A. Liebsch, Electronic Excitations at Metal Surfaces (Plenum, 1997).
  25. N. D. Mermin, “Lindhard dielectric function in the relaxation time approximation,” Phys. Rev. B 1, 2362–2363 (1970). [CrossRef]
  26. G. D. Mahan, Many-Particle Physics (Plenum, 1990), Chapter 5.
  27. J. M. McMahon, S. K. Gray, and G. C. Schatz, “Nonlocal optical response of metal nanostructures with arbitrary shape,” Phys. Rev. Lett. 103, 097403 (2009). [CrossRef]
  28. C. David and F. J. G. de Abajo, “Spatial nonlocality in the optical response of metal nanoparticles,” J. Phys. Chem. C 115, 19470–19475 (2011). [CrossRef]
  29. C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072–1074 (2012). [CrossRef]
  30. P. J. Feibelman, “Surface electromagnetic fields,” Prog. Surf. Sci. 12, 287–407 (1982). [CrossRef]
  31. K. Artmann, “Berechnung der seitenversetzung des totalreflektierten stranles,” Ann. Phys. 2, 87–102 (1948). [CrossRef]
  32. U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer, 1995).
  33. J. B. Götte, A. Aiello, and J. P. Woerdman, “Loss-induced transition of the Goos–Hänchen effect for metals and dielectrics,” Opt. Express 16, 3961–3969 (2008). [CrossRef]
  34. Note that in order to limit the number of figures in our paper, the plots of the dielectric functions are not included but are available upon request.
  35. W. Ekardt, “Size-dependent photoabsorption and photoemission of small metal particles,” Phys. Rev. B 31, 6360–6370 (1985). [CrossRef]
  36. L. Liebsch, “Surface-plasmon dispersion and size dependence of Mie resonance: silver versus simple metals,” Phys. Rev. B 4811317 (1993). [CrossRef]
  37. J. Tiggesbaumker, L. Koller, K. H. Meiwes-Broer, and A. Liebsch, “Blue shift of the Mie plasma frequency in Ag clusters and particles,” Phys. Rev. A 48, R1749–R1752 (1993). [CrossRef]
  38. S. Palomba, L. Novotny, and R. E. Palmer, “Blue-shifted plasmon resonance of individual size-selected gold nanoparticles,” Opt. Commun. 281, 480–483 (2008). [CrossRef]
  39. R. Fuchs, R. G. Barrera, and J. L. Carrillo, “Spectral representations of the electron energy loss in composite media,” Phys. Rev. B 54, 12824–12834 (1996). [CrossRef]

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